I also have lower back problems and can't do crunches (heck I can't even sleep comfortably) on a floor or mat.
I have been using the abdominal machine at the gym I go to (military gym) and have noticed a tightening of my abdominal muscles. This is the kind where you sit, knees bent, and push the bar directly out in front, then lean back and forward against the weight your arms are holding out. However, I overdid it yesterday and pulled a muscle in my upper back, causing extreme pain over my left shoulderblade near my spine. Still dealing with the pain from that - although it is manageable today.
I won't be using the machine again for a while, will instead focus on cardio workouts until I've lost a little more fat and gained a little more muscle tone.
I found
this website for ab exercises including the ball, which is something I think I might get after my back heals up some.